How to subdivide concave face into quads
Download TinyCAD script from GitHub:
https://github.com/zeffii/mesh_tiny_cad

File > User Preferences > Add-ons > Install from file...
choose the zip file

Edit mode + Edge select > C
select an edge, and another one you'd like it to extend to.
Right-click to finalize selection.  

W to bring up specials menu > TinyCAD > VTX | AUTO  

I'm not having much luck with this script over here.
I'm not a pro at it, but I'm hoping it gets you in the right direction.  

You might need to tweak it, but at least if gives something to start from.
Or file a bug-report on GitHub, if it's not doing what you need.  

I've used a similar feature in drafting class, so I get what you're going for.
Hope it does better for you.